Hi all,

I've been using Faraday's law to find the EMF in a coil of wire in a changing magnetic field.

EMF = -N (change in mag flux/change in time) for N loops​

I'm finding that the EMF is always positive regardless of whether the change in flux is positive or negative. I'm wondering at what point we choose to ignore the negative sign and why?

What I've been considering...
• I was thinking it could be a vector/scalar issue. But scalars can be negative.
• I think that the sign of the change in flux is important (Lenz's law etc).
• I understand that conservation of energy requires the induced EMF to oppose the change in flux. So the negative sign is important in the law.
• So is the sign of the EMF not important for some reason?

marcusl
Gold Member
The sign in the equation is correct, as required to satisfy Lenz's Law (you are completely right about that). If you always see the same sign, then you aren't doing your experiment correctly or aren't interpreting your results correctly.

jtbell
Mentor
The minus sign has to do with the direction of the emf: whether it is in one direction or the other, going around the coil, which in turn determines the direction of the induced current. Usually, in an introductory course, we figure out the direction of the emf or current non-mathematically, using a right-hand rule, in which case the minus sign in Faraday's Law is irrelevant as far as calculating the magnitude of the emf or current is concerned. When I teach Faraday's Law at that level, I always write it in terms of magnitudes, using absolute-values, and omit the minus sign.

In intermediate or advanced classes, we write out the emf and the flux as integrals:

$$\int {\vec E \cdot d \vec l} = - \frac{d}{dt} \int {\vec B \cdot d \vec a}$$

where the first integral is a line integral around the loop (coil), and the second integral is a surface integral over a surface bounded by the loop. Without the minus sign, the direction of integration around the loop is related to the orientation of the surface (direction of $d \vec a$) by the right-hand rule. To make things come out right physically, we need to include the minus sign.

Thanks for the reply marcusl. This is not from an experiment, it is from questions in a text book and the text book always gives the EMF as positive regardless of the sign of the change in magnetic flux.

If I understand jtbell correctly this is because they are only interested in the magnitude of the EMF (even though they don't state it).

I think I'll need to understand more about how the direction of the change in flux relates to the direction of the EMF before I'll really be comfortable with this.

Thanks again for the help.

marcusl